Effect of the Quadrupole–Monopole Interaction on Chaos in Compact Binaries

Abstract

AbstractThe dynamics of a post‐Newtonian Lagrangian of spinning compact binaries, including the Newtonian, post‐Newtonian, spin‐orbit, spin‐spin, and quadrupole–monopole interaction contributions are investigated herein. According to the Euler–Lagrangian equations, exact and approximate equations of motion can be written. Numerical computations show that the constants of motion can reach satisfactory accuracies in the exact equations but rather poor accuracies in the approximate equations. Similar to the spin–orbit coupling or the spin–spin coupling, the quadrupole–monopole interaction plays a role in some spin effects that lead to the precession of orbits. With the increase in quadrupole–monopole and extension of integration, the orbits precess strongly and the difference in the precession of orbits between the two sets of equations increases. The quadrupole–monopole interaction can also cause the chaoticity of spinning compact binaries. When it increases, chaos is strong under some circumstances in the exact equations but not in the approximate equations.